semantic rate-distortion analysis

This work addresses the neglect of high computational complexity in existing deep learning–based semantic communication systems and the lack of a theoretical characterization of the trade-off among transmission rate, semantic fidelity, and model complexity. To this end, the authors propose a Rate–Distortion–Complexity (RDC) theoretical framework that extends classical rate–distortion theory to semantic communication scenarios. The framework introduces a semantic distance combining bit-wise distortion and statistical divergence, and defines model complexity via the Minimum Description Length and Information Bottleneck principles. Closed-form achievable rates are derived for Gaussian and binary semantic sources, revealing the underlying triple trade-off. Empirical validation on real image and video data demonstrates the efficacy of the theoretical analysis, with the proposed complexity metric showing strong correlation with actual computational overhead, thereby enabling efficient semantic communication system design under resource constraints.

This work addresses the challenge of semantic communication under limited information rates and computational resources, where the encoder and decoder pursue misaligned objectives. Focusing on strategic Gaussian semantic compression, the study jointly optimizes their distinct quadratic objectives under a rate constraint by designing the posterior covariance, modeling the decoder as an MMSE estimator, and introducing a “semantic water-filling” principle alongside a Gaussian persuasion mechanism. Theoretical analysis reveals that model depth and inference time yield exponential gains in semantic accuracy and demonstrates that multimodal observations eliminate the geometric-mean penalty inherent in remote encoding. By establishing a theory of Gaussian optimality under objective misalignment, this work provides an information-theoretic foundation for resource-constrained efficient AI systems and offers a novel interpretation for posterior design in multimodal large language models.

This study addresses the dual-fidelity rate–distortion trade-off for structured semantic sources in task-oriented communication. By restricting to deterministic intra-class encoding mappings and integrating conditional mean decoding with the Lloyd–Max stationarity conditions, the paper derives fundamental rate–distortion characteristics. It innovatively constructs the first dual-purpose feasibility band tailored to such semantic sources, revealing upper and lower bounds on achievable communication rates under non-single-letter fidelity criteria and their dependence on partition cardinality, thereby extending the Shannon–Kolmogorov (SK) framework. Theoretically, it proves that the intra-class SK rate is no less than the maximum of the corresponding Shannon rate–distortion function. In an aggregation validation scenario, a feasibility band of width $\log_2(K_{\max}/K_{\min})$ bits is obtained, with empirical validation provided through a smart grid economic dispatch case study.

Existing semantic communication research overemphasizes transmission fidelity while neglecting the fundamental fact that AI task performance is determined by model training—leading to a “fidelity-constraint paradox.” Method: This paper proposes a goal-oriented semantic communication paradigm that models and proactively estimates how communication-induced distortions—introduced by semantic compression—affect AI task accuracy. It innovatively extends rate-distortion theory to semantic communication by quantifying distributional shifts between original and distorted data, thereby establishing a distortion–accuracy mapping. The framework integrates distribution-shift modeling, semantics-aware compression, and joint communication-computation optimization under network constraints (e.g., bandwidth, latency). Contribution/Results: Experiments demonstrate that the proposed method significantly outperforms fidelity-driven baselines, improving task accuracy by 12.6%–28.3% under identical resource budgets, while guaranteeing empirically validated accuracy for downstream AI tasks.

Semantic communication lacks a unified theoretical framework. This work formally defines its fundamental problem and identifies two core challenges: “language utilization” (efficiently leveraging existing linguistic structures) and “language design” (constructing optimal semantic representations). Method: For language utilization, we establish three pathways—semantic encoding, semantic decoding, and collaborative semantic coding. For language design, we embed it within a joint source-channel coding framework. We introduce the semantic distortion–cost region as a novel performance evaluation paradigm and develop end-to-end semantic distortion metrics alongside a joint optimization theory. Leveraging information theory, rate-distortion analysis, and semantic modeling, we rigorously characterize the achievable performance bounds for all three pathways. Contribution/Results: This study provides the first systematic theoretical foundation for semantic communication, establishes its fundamental performance limits, and delivers a verifiable design benchmark—enabling principled analysis and optimization of semantic systems.

This study addresses the problem of compressing random variables under three simultaneous constraints: distortion (fidelity), perceptual naturalness, and a newly introduced deception constraint that requires reconstructed samples to appear as if drawn from a target distribution. By incorporating this deception constraint into the classical rate–distortion framework, the work extends traditional information-theoretic analysis to cross-distribution camouflage scenarios. Leveraging an information-theoretic formulation combined with distributional distance measures, the authors derive fundamental limits of compression under deception and establish a precise trade-off among rate, distortion, and deception. This theoretical advance provides a new foundation for applications such as privacy-preserving data release and adversarial data obfuscation.

Traditional rate–distortion theory struggles to capture the requirements of learning-driven applications concerning perceptual quality and semantic fidelity. This work formalizes perceptual fidelity as a distributional similarity constraint and introduces, for the first time, the rate–distortion–perception function (RDPF), which unifies the treatment of both discrete and continuous sources. The paper establishes fundamental connections between the RDPF and key statistical divergences—namely f-divergences, α-divergences, and the Wasserstein metric. Leveraging tools such as alternating minimization, Newton’s method, and convex optimization, the authors efficiently compute the RDPF in analytically tractable settings, including Gaussian sources. By delineating the fundamental limits of perception-aware compression and providing a computable theoretical framework, this study lays the groundwork for neural compression and perception-driven network control.

This work addresses the lack of clear information-theoretic guidance in existing perceptual lossy source coding, which has led to overreliance on opaque deep learning models. Building upon rate–distortion–perception theory, the study reformulates information-theoretic limits from mere performance benchmarks into constructive design principles. Through an intuitive unit-circle teaching model, it elucidates core mechanisms—including codec architecture, trade-off relationships, and universal representations—and clarifies the role of common randomness in unifying single-shot and asymptotic settings. The proposed framework bridges perceptual coding with classical lossy compression, offering a theoretically grounded foundation for interpretable and implementable system design along with principled optimization pathways.

This work addresses the perceptual degradation—such as blurriness or unnatural artifacts—that commonly arises in conventional lossy compression under fidelity constraints, a challenge also prevalent in distributed coordination under limited communication. For the first time, it establishes an information-theoretic correspondence between realism constraints in compression and distributed coordination problems, highlighting the pivotal roles of common randomness and distribution matching. By introducing novel paradigms including batch discriminators and algorithmic realism, and integrating strong distribution matching models, the soft covering lemma, and discriminator-based perceptual evaluation, the paper formulates a unified rate–distortion–perception tradeoff framework. This framework provides both theoretical foundations and new directions for enhancing perceptual reconstruction quality and enabling efficient distributed coordination.